Skip to main content
SpringerLink
Log in

Subelliptic, second order differential operators

  • Special Year Papers
  • Conference paper
  • First Online:
Complex Analysis III

Part of the book series: Lecture Notes in Mathematics ((LNM,volume 1277))

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 34.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 46.00
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Ancona, A., Principe de Harnack à la frontière et théorème de Fatou pour un opérateur elliptique dans un domaine Lipschitzien, Ann. Inst. Fourier 28(4), 169–213(1978).

    Article  MathSciNet  MATH  Google Scholar 

  2. Axler, S. and Shields, A.L., Univalent multipliers of the Dirichlet space, preprint.

    Google Scholar 

  3. Bony, J.-M., Principe du maixmum, inégalité de Harnack et unicité du problème de Cauchy pour les opérateurs elliptiques dégénérés, Ann. Inst. Fourier 19(1), 277–304(1969).

    Article  MathSciNet  MATH  Google Scholar 

  4. Davies, E.B., Explicit constants for Gaussian upper bounds on heat kernels, preprint.

    Google Scholar 

  5. Derridj, M., Un problème aux limites pour une classe d'opérateurs hypoelliptiques du second ordre, Ann. Inst. Fourier 21(4), 99–148(1971).

    Article  MathSciNet  MATH  Google Scholar 

  6. Fabes, E., Jerison, D. and Kenig, C., Boundary behavior of solutions to degenerate elliptic equations, Proceedings of the Conference on Harmonic Analysis in Honor of Antoni Zygmond, Wadworth Math. Series, 577–589(1981).

    Google Scholar 

  7. Fefferman, C.L. and Phong, D.H., Subelliptic eigenvalue problems, Proceedings of the Conference on Harmonic Analysis in Honor of Antoni Zygmund, Wadsworth Math. Series, 590–606(1981).

    Google Scholar 

  8. Fefferman, C.L. and Sánchez-Calle, A., Fundamental solutions for second order subelliptic operators, Ann. of Math. 124, 247–272(1986).

    Article  MathSciNet  MATH  Google Scholar 

  9. Fichera, G., On a unified theory of boundary value problems for elliptic-parabolic equations of second order. In Boundary problems in Differential Equations, Univ. of Wisconsin Press, Madison, 97–120(1973).

    Google Scholar 

  10. Folland, G.B., A fundamental solution for a subelliptic operator, Bull. Amer. Math. Soc. 79, 373–376(1973).

    Article  MathSciNet  MATH  Google Scholar 

  11. Folland, G.B., Subelliptic estimates and function spaces on nilpotent Lie groups, Arkiv för Mat. 13, 161–207(1975).

    Article  MathSciNet  MATH  Google Scholar 

  12. Folland, G.B. and Stein, E.M., Estimates for the ∂ b -complex and analysis on the Heisenberg group, Comm. Pure Appl. Math. 27, 429–522(1974).

    Article  MathSciNet  MATH  Google Scholar 

  13. Gaveau, B., Principe de moindre action, propagation de la chaleur et estimées sous elliptiques sur certains groupes nilpotents, Acta Math. 139, 95–153(1977).

    Article  MathSciNet  Google Scholar 

  14. Grushin, V., On a class of hypoelliptic pseudodifferential operators degenerate on a submanifold, Math. USSR Sbornik 13, 155–185(1971).

    Article  MATH  Google Scholar 

  15. Hardy, G.H., Littlewood, J.E. and Pólya, G., Inequalities, Cambridge University Press (1952).

    Google Scholar 

  16. Hörmander, L., Hypoelliptic second order differential equations, Acta Math. 119, 147–171(1967).

    Article  MathSciNet  MATH  Google Scholar 

  17. Hörmander, L.: Subelliptic operators, Annals of Math. Studies 91, Princeton Univ. Pres, 127–208 (1978).

    Google Scholar 

  18. Hueber, H. Further examples of irregular domains for some hypoelliptic operators, preprint.

    Google Scholar 

  19. Jerison, D., Counterexamples to the Poincaré inequality, Proc. Amer. Math. Soc. 8, 207–210(1957).

    MathSciNet  Google Scholar 

  20. Jerison, D., The Dirichlet problem for the Kohn Laplacian on the Heisenberg group, I. II, Jour. of Funct. Anal. 43, 97–142, 224–257(1981).

    Article  MathSciNet  MATH  Google Scholar 

  21. Jerison, D., The Poincaré inequality for vector fields satisfying Hörmander's condition, Duke Math. Jour. 53, 503–523(1986).

    Article  MathSciNet  MATH  Google Scholar 

  22. Jerison, D. and Kenig, C., Boundary behavior of harmonic functions in nontangentially accessible domains, Advances in Math. 46, 80–147(1982)

    Article  MathSciNet  MATH  Google Scholar 

  23. Jerison, D. and Sánchez-Calle, A., Estimates for the heat kernel for a sum of squares of vector fields, to appear in Indiana Univ. J. of Math.

    Google Scholar 

  24. Kohn, J.J., Boundaries of complex manifolds, Proc. conf. on complex manifolds (Minneapolis), Springer-Verlag, N.Y., 81–94(1965).

    Google Scholar 

  25. Kohn, J.J., Pseudodifferential operators and hypoellipticity, Proc. Symp. Pure Math. 23, 61–69(1973).

    Article  MathSciNet  Google Scholar 

  26. Kohn, J.J.: Estimates for ∂ b in compact pseudoconvex CR manifolds, Proc. Symp. Pure Math. 43, 207–217(1985).

    Article  MathSciNet  Google Scholar 

  27. Kohn, J.J. and Nirenberg, L., Degenerate elliptic-parabolic equations of second order, Comm. Pure Appl. Math. 20, 797–872(1967).

    Article  MathSciNet  MATH  Google Scholar 

  28. Kohn, J.J. and Rossi, H., On the extension of holomorphic functions from the boundary of a complex manifold, Ann. Math. 81, 451–472(1965).

    Article  MathSciNet  MATH  Google Scholar 

  29. Kusuoka, S. and Stroock, D., Applications of the Malliavin calculus, part III, preprint.

    Google Scholar 

  30. Kusuoka, S. and Stroock, D., Long time estimates for the heat kernel associated with a uniformly subelliptic symmetric second order operator, preprint.

    Google Scholar 

  31. Léandre, R., Estimation en temps petit de la densité d'une diffusion hypoelliptique, C.R. Acad. Sc. Paris, t. 301, Série I, 17, 801–804(1985).

    MATH  Google Scholar 

  32. Melrose, R., Propagation for the wave group of a positive subelliptic second order differential operator, preprint.

    Google Scholar 

  33. Metivier, G., Fonction spectrale et valeurs propres d'une classe d'opérateurs non elliptiques, Comm. in P.D.E. 1(5), 467–519(1976).

    Article  MathSciNet  MATH  Google Scholar 

  34. Moser, J., On Harnack's theorem for elliptic differential equations, Comm. Pure Appl. Math. 14, 577–591(1961).

    Article  MathSciNet  MATH  Google Scholar 

  35. Muckenhoupt, B., Hardy's unequality with weights, Studia Math. 44, 31–38(1972).

    MathSciNet  MATH  Google Scholar 

  36. Nagel, A., Stein, E.M. and Wainger, S., Balls and metrics defined by vector fields I: Basic properties, Acta Math. 155, 103–147(1985).

    Article  MathSciNet  MATH  Google Scholar 

  37. Oleinik, O. and Radkevic, E., Second order equations with nonnegative characteristic form, Amer. Math. Society, Providence, R.I. (1973).

    Book  Google Scholar 

  38. Phillips, R.S. and Sarason, L., Elliptic-Parabolic equations of the second order, Jour. of Math. and Mech. 17, 891–917(1968).

    MathSciNet  MATH  Google Scholar 

  39. Rothschild, L. and Stein, E.M., Hypoelliptic differential operators and nilpotent Lie groups, Acta Math. 137, 247–320(1977).

    Article  MathSciNet  MATH  Google Scholar 

  40. Sánchez-Calle, A., Fundamental solutions and geometry of the sum of squares of vector fields, Invent. Math. 78, 143–160(1984).

    Article  MathSciNet  MATH  Google Scholar 

  41. Stegenga, D., Multipliers of the Dirichlet space, Illinois J. Math. 24, 113–139(1980).

    MathSciNet  MATH  Google Scholar 

  42. Stein, E.M., Singular integrals and differentiability properties of functions, Princeton Univ. Press (1970).

    Google Scholar 

  43. Stroock, D. and Taniguchi, S., Regular points for the first boundary problem associated with degenerate elliptic equations, preprint.

    Google Scholar 

  44. Xu, C.-J., Opérateurs sous-elliptiques et regularité des solutions d'équations aux derivées partielles non linéaires du second ordre en deux variables, U. of Paris-Sud, preprint.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Mathematics, Massachusetts Institute of Technology, 02139, Cambridge, Massachusetts

    David Jerison & Antonio Sánchez-Calle

Authors
  1. David Jerison
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Antonio Sánchez-Calle
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Carlos A. Berenstein

Rights and permissions

Reprints and permissions

Copyright information

© 1987 Springer-Verlag

About this paper

Cite this paper

Jerison, D., Sánchez-Calle, A. (1987). Subelliptic, second order differential operators. In: Berenstein, C.A. (eds) Complex Analysis III. Lecture Notes in Mathematics, vol 1277. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0078245

Download citation

  • DOI: https://doi.org/10.1007/BFb0078245

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-18355-6

  • Online ISBN: 978-3-540-47893-5

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation